Integral torsion points on abelian varieties over function fields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915758061125632 |
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| author | de Jong, Robin Looper, Nicole Shokrieh, Farbod |
| author_facet | de Jong, Robin Looper, Nicole Shokrieh, Farbod |
| contents | We prove an analogue, over global function fields, of a conjecture due to Su-Ion Ih concerning the non-Zariski density of torsion points on abelian varieties that are integral with respect to a given non-special divisor. Along the way, we establish a Tate--Voloch type theorem for abelian varieties over completions of global function fields, which allows us to obtain a logarithmic equidistribution result for Galois orbits of torsion points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19757 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integral torsion points on abelian varieties over function fields de Jong, Robin Looper, Nicole Shokrieh, Farbod Number Theory Algebraic Geometry 11G10, 11G35, 11G50, 14G40, 14K12 We prove an analogue, over global function fields, of a conjecture due to Su-Ion Ih concerning the non-Zariski density of torsion points on abelian varieties that are integral with respect to a given non-special divisor. Along the way, we establish a Tate--Voloch type theorem for abelian varieties over completions of global function fields, which allows us to obtain a logarithmic equidistribution result for Galois orbits of torsion points. |
| title | Integral torsion points on abelian varieties over function fields |
| topic | Number Theory Algebraic Geometry 11G10, 11G35, 11G50, 14G40, 14K12 |
| url | https://arxiv.org/abs/2601.19757 |